## 1st Bank PO level Question Set, 1st on topic Permutation and Combination

This is the 1st question set of 10 practice problem exercise for Bank PO exams and 1st on topic Permutation and Combination. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set for gaining maximum benefits from this resource.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts in the topic area
- is adequately fast in mental math calculation
- should try to solve each problem using the basic and rich concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving is done in the fourth layer. You need to use **your problem solving abilities** to gain an edge in competition.

We list below the few important formulas for permutation and combination. If you already know, you may skip.

### Basic formulas on permutation and combination

**First case:** **Permutation** (or number of possible ordered arrangements) of $r$ **distinct objects** out of $N$ distinct objects. It is,

$^NP_r=\displaystyle\frac{N\text{!}}{(N-r)\text{!}}$, where Factorial $N$, expressed as $N\text{!}$, is equal to the product of integers starting from $N$ decreasing by 1 and ending with 1.

In other words,

$N!=N\times{(N-1)}\times{(N-2)}\times{...}\times{2}\times{1}$.

With this knowledge we can express,

$^NP_r=N\times{(N-1)}\times{(N-2)}\times{...}\times{(N-r+1)}$, cancelling out $(N-r)\text{!}$ between numerator and denominator.

For example, permutation of 3 distinct objects out of 8 distinct objects will be,

$^8P_3=8\times{7}\times{6}$, the denominator $(8-3)\text{!}=5\text{!}$ is cancelled out with part of the numerator.

**Second case: ** **Permutation** of $r$ objects out of $N$ objects with $q$ objects in the set of $N$ **objects alike** or same,

$^NP_r\text{ with q alike}=\displaystyle\frac{N\text{!}}{(N-r)\text{!}\times{q\text{!}}}$.

**Third case:** **Combination or selection** of $r$ distinct objects out of $N$ distinct objects,

$^NC_r=\displaystyle\frac{N\text{!}}{r\text{!}\times{(N-r)\text{!}}}={^NC_{N-r}}$.

For more details and clear understanding of the concepts, you should refer to our extensive tutorial,

* Permutation and Combination with exercises*.

### 1st question set - 10 problems for Bank PO exams: 1st on topic Permutation and Combination - time 12 mins

**Problem 1.**

Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

- 76
- 80
- 84
- 96
- None of the above

**Problem 2.**

In how many different way can the letters of the word SOFTWARE be arranged in such a way that the vowels always come together?

- 13440
- 120
- 1440
- 360
- None of the above

**Problem 3.**

A team of 5 children is to be selected out of 4 girls and 5 boys so that it contains at least 2 girls. In how many ways the selection can be made?

- 105
- 120
- 60
- 100
- None of the above

**Problem 4.**

In how many different ways a group of 4 men and 4 women be formed out of 7 men and 8 women?

- 105
- 2450
- 1170
- Cannot be determined
- None of the above

**Problem 5.**

On a shelf there are 3 books on Management, 4 books on Economics and 4 books on Statistics. In how many different ways the books can be arranged so that the books on Economics are kept together?

- 5040
- 120960
- 40320
- 967680
- None of the above

#### Problem 6.

A committee of 5 members is to be formed out of 4 students, 3 teachers and 2 sports coaches. In how many ways can the committee be formed if the committee should consist of 2 students, 2 teachers and 1 sports coach?

- 25
- 9
- 64
- 36
- None of the above

**Problem 7.**

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels be formed?

- 24400
- 210
- 21300
- 25200
- None of the above

**Problem 8.**

A committee of 12 persons is to be formed from 9 women and 8 men. In how many ways this can be done if at least 5 women have to be included in the committee?

- 6000
- 6005
- 6010
- 6062
- None of the above

**Problem 9.**

Two girls and 4 boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

- 360
- 720
- 480
- 240
- None of the above

**Problem 10.**

In how many different ways can the letters in the word BANKING be arranged?

- 2520
- 5040
- 5080
- 2540
- None of the above

You may refer to the detailed solutions in * Bank PO level Solutions 1 on Permutation Combination 1*.

### Answer to the questions

**Problem 1.** Answer: Option b: 80.

**Problem 2.** Answer: Option e: None of the above.

**Problem 3.** Answer: Option a: 105.

**Problem 4.** Answer: Option b: 2450.

**Problem 5.** Answer: Option d: 967680.

**Problem 6.** Answer: Option d: 36.

**Problem 7.** Answer: Option d: 25200.

**Problem 8.** Answer: Option d: 6062.

**Problem 9.** Answer: Option c: 480.

**Problem 10.** Answer. Option a: 2520.

### Further reading resources

**Tutorial on Permutation and Combination with exercise problems**

**Solutions to the exercise problems on Permutation and combination**

**Bank PO level Solution set 2 on Permutation and Combination 2**

**Bank PO level Question set 2 on Permutation and Combination 2**

**Bank PO level Solutions 1 on Permutation combination 1**

**Bank PO level Question set 1 on Permutation combination 1**